{"status": "success", "data": {"description_md": "The function $f$ has the property that, for each real number $x,$ $$ f(x)+f(x-1) = x^2. $$ If $f(19)=94,$ what is the remainder when $f(94)$ is divided by 1000?\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>The function <span class=\"katex--inline\">f</span> has the property that, for each real number <span class=\"katex--inline\">x,</span> <span class=\"katex--display\"> f(x)+f(x-1) = x^2. </span> If <span class=\"katex--inline\">f(19)=94,</span> what is the remainder when <span class=\"katex--inline\">f(94)</span> is divided by 1000?</p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "1994 AIME Problem 3", "can_next": true, "can_prev": true, "nxt": "/problem/94_aime_p04", "prev": "/problem/94_aime_p02"}}